We present a hybrid algorithm that combines a Newton iteration process with the continuation code PITCON ([RB83]). The proposed algorithm is tested by using standard sets of examples ([Bus80], [Hie82], [Sha85] and others), 36 different problems that combined with different scaling conditions and initial points give 327 problems. The algorithm solves more than 98% of the problems as opposed to 61% solved by the code HYBRD from MINPACK [MGH80].